Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article A System of Nonlinear Operator Equations for a Mixed Family of Fuzzy and Crisp Operators in Probabilistic Normed Spaces | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 152978 16 pages doi 2010 152978 Research Article A System of Nonlinear Operator Equations for a Mixed Family of Fuzzy and Crisp Operators in Probabilistic Normed Spaces Yeol Je Cho 1 Heng-you Lan 2 and Nan-jing Huang3 1 Department of Mathematics Education and the RINS Gyeongsang National University Chinju 660-701 South Korea 2 Department of Mathematics Sichuan University of Science Engineering Zigong Sichuan 643000 China 3 Department of Mathematics Sichuan University Chengdu Sichuan 610064 China Correspondence should be addressed to Heng-you Lan hengyoulan@ Received 8 January 2010 Accepted 23 March 2010 Academic Editor Yuming Xing Copyright 2010 Yeol Je Cho et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. By using a random version of the theory of contractor introduced by Altman we introduce and study a system of nonlinear operator equations for a mixed family of fuzzy and crisp operators in probabilistic normed spaces. We construct some new iterative algorithms for solving this kind of nonlinear operator equations. We also prove some new existence theorems of solutions of a new system of nonlinear operator equations for a mixed family of fuzzy and crisp operators and some new convergence results of sequences generated by iterative algorithms under joint orbitally complete conditions. 1. Introduction Altman 1 2 introduced the theory of contractor and contractor direction which has a very strong significant for the study of existence and uniqueness for solving nonlinear operator equations in Banach spaces. The theory of contractor offers a unified approach to a very large class of iterative methods including the most important ones. Chang 3 introduced the concept of probabilistic contractor .
